# Weisfeiler-Lehman Kernel

The Weisfeiler-Lehman kernel is an iterative integration of neighborhood information.

We initialize the labels for each node using its own node degree. At each step, we take the neighboring node degrees to form a [[multiset]] Multiset, mset or bag A bag is a set in which duplicate elements are allowed. An ordered bag is a list that we use in programming. . At step $K$, we have the multisets for each node. Those multisets at each node can be processed to form an representation of the graph which is in turn used to calculate statistics of the graph.

This iteration can be used to test if two graphs are isomorphism^{1}.

- Shervashidze2011 Shervashidze N, Schweitzer P, van Leeuwen EJ, Mehlhorn K, Borgwardt KM. Weisfeiler-Lehman Graph Kernels. J Mach Learn Res. 2011;12: 2539–2561. Available: https://dl.acm.org/doi/10.5555/1953048.2078187
- Hamilton2020 Hamilton WL. Graph Representation Learning. Morgan & Claypool Publishers; 2020. pp. 1–159. doi:10.2200/S01045ED1V01Y202009AIM046

L Ma (2021). 'Weisfeiler-Lehman Kernel', Datumorphism, 09 April. Available at: https://datumorphism.leima.is/cards/graph/graph-weisfeiler-lehman-kernel/.